## Wednesday, June 8, 2011

### June Vacation Chap 9.2 RATE (L4) Self-Paced Learning

1. Mathematics Textbook 1B
(a) Go through Chapter 9 (p9 to p11)
(b) Attempt Exercise 9.2 Q1 to Q10.

2. ACELearning Portal: eLearning Portal
> Subject: Secondary 1 Express
> Ratio, Rate and Speed: Choose Rate

(a) Go through video lessons: Rate, Average Rate, Example 1, Example 2
Note: An email has been sent to all students via the AceLearning

1a - \$3.50
1b - 72 vases/day
1c - 47 words/min
1d - \$80/m²
1e - 4kg/m
1f - 60g/egg

2a - \$23/hr
2b - \$920/week

3a - 9km/litre
3b - \$1.20/litre

4a -87.5g
4b - 125cm³

5a - \$15
5b - \$150

6a - \$22.50/m²
6b - \$450

7a - 27 litres/minute
7b - 3 minutes

8a - \$26/kg
8b - 25g

9a - \$201 600
9b - \$4200/m²

10a - 19.3g
10b - 2cm x 2cm x 2cm = 8cm³

27cm³ -> 521.1g
8cm³ -> 8/27 x 521.1g = 154.4g
154.4g > 120g

Explanation : No, it is not made from pure gold. The gold cube is not pure gold as it is lighter than pure gold when it is at 8cm³. At 8cm³, the pure gold should weigh in at 154.4g. This gold cube weighs 120g which is lighter than the pure gold cube. Therefore, it is not pure gold.

2. ============================
Exercise 9.2
============================
1a) A 2-litre bottle of peanut oil costs \$7

2 litre of peanut oil cost -> \$7
1 litre of peanut oil cost -> \$7 ÷ 2 = \$3.50

The price rate is \$3.50 / litre
============================
1b) A company produces 360 vases in 5 days.

5 days -> 360 vases
1 day -> 360 ÷ 5 = 72 vases

The rate of production is 72 vases/day.
============================
1c) Huili typed 376 words in 8 minutes.

8 minutes -> 376 words
1 minute -> 376 ÷ 8 = 47 words

Her rate of typing is 47 words/min
============================
1d) A carpet of area 3m² costs \$240.

3m² -> \$240
1m² -> \$240 ÷ 3 = \$80

The price rate is \$80 / m²
============================
1e) The mass of a 2.5-m metal bar is 10kg.

10kg / 2.5m = 4kg / m

The rate of mass is 4 kg/m
============================
1f) The mass of 12 eggs is 720g.

12 eggs -> 720g
1 egg -> 720g ÷ 12 = 60g

The rate of mass is 60g/egg.
============================
============================
2) Rahman works 5 days a week and 8 hours a day. His daily wage is \$184.
a) Find his hourly wage rate.

\$184 ÷ 8 = \$23 / hr

His hourly wage rate is \$23/hr
-----------------------------------------
a) Find his weekly wage rate.

\$184 x 5 = \$920/week
============================
============================
3) A car travelled 225 km on 25 litres of petrol. The price of petrol consumed was \$30.
a) Find the rate of petrol consumption in km/litre.

225/25litre = 9km/litre

The rate of petrol consumption is 9km/litre.
-----------------------------------------
a) What was the price of petrol per litre?

\$30/25 litre = \$1.20/litre

The price of petrol is \$1.20/litre
============================
============================
4) There are 6 wooden cubes, each of side 5cm. Their total mass is 525g. Find the mass per :
a) cube,

525g ÷ 6 = 87.5g

The mass of one cube is 87.5g.
-----------------------------------------
b) cm³ of cube.

5cm x 5cm x 5cm = 125cm³

The volume of one cube is 125cm³.
============================
Further Practice
============================

5)John spent \$120 on 8 concert tickets.
a) Find the price per ticket.

8 Concert Tickets -> \$120
1 Concert Ticket -> \$120 ÷ 8 = \$15

The price of 1 concert ticket is \$15.
-----------------------------------------
b) Find the price of 10 tickets.

8 Concert Tickets -> \$120
10 Concert Tickets -> 10/8 x \$120 = \$150

10 Concert Tickets costs \$150.
============================
============================
6) The price of laying 12m² of floor tiles is \$270.
a) Find the price of laying floor tiles per m².

12m² -> \$270
1m² -> \$22.50
The price of laying floor is \$22.50/m².
-----------------------------------------
b) Find the price of laying 20 m² of floor tiles.

12m² -> \$270
20m² -> 20/12 x \$270 = \$450

The price of laying 20m² is \$450
============================
============================
7) A pipe delivers 9 litre of water in 20 seconds.
a) Find the amount of water it delivers per minute.

1 minute = 60 seconds
60 seconds ÷ 20 seconds = 3
3 x 9 litres = 27 litres

The pipe can deliver 27 litres per minute.
-----------------------------------------
b) An empty fish tank is 60 cm long, 45 cm wide and 30 cm high. How long does it take for the pipe to fill the empty tank completely with water?
(1 litre = 1000 cm³)

Volume = 60cm x 45 cm x 30 cm = 81000cm³
81000cm³ = 81 litres
81 litre ÷ 27 litre = 3 minutes

It would take 3 minutes to fill the empty tank.

3. WORKINGS (Part 2)

============================
Maths @ Work
============================
8) A 500-g pack of fertiliser that costs \$13 can be applied to 20 m² of lawn.
a) What is the cost of the fertiliser per kg?

1kg = 1000g
1000g ÷ 500g = 2
2 x \$13 = \$26

The fertiliser cost \$26/kg
-----------------------------------------
b) Find the mass of the fertiliser that can be applied to 1m² of lawn.

500g ÷ 20m² = 25g/m²

25g of fertiliser can be applied to 1m² of lawn.
-----------------------------------------
a) A rectangular lawn measures 15m by 8m. Find the mass and cost of the fertiliser required for the lawn.

15m x 8m = 120m²
120m² ÷ 20m² = 6
6 x \$13 = \$78
6 x 500g = 3000g
3000g = 3kg

The cost and the mass of the fertiliser is \$78 and 3kg respectively.
============================
============================
9) The price of an apartment of area 120 m² is \$504 000. Jenny and her mother shared the cost of such an apartment in the ratio 2 : 3.
a) How much did Jenny pay?

2 + 3 = 5
2/5 x \$504 000 = \$201 600

Jenny paid \$201 600 for the apartment
-----------------------------------------
b) What was the price per m² of the apartment?

\$504 000 ÷ 120m² = \$4200/m²

1m² costs \$4200
============================
============================
10) A pure gold cube is of side 3cm. Its mass is 521.1 g.
a) Find the mass of pure gold per cm³.

3cm x 3cm x 3cm = 27 cm³
27cm³ -> 521.1g
1cm³ -> 19.3g

1cm³ of pure gold weighs 19.3g
-----------------------------------------
b) Another gold cube is of side 2cm. Its mass is 120 g. Is it made of pure gold? Explain briefly.

2cm x 2cm x 2cm = 8cm³

27cm³ -> 521.1g
8cm³ -> 8/27 x 521.1g = 154.4g
154.4g > 120g

Explanation : No, it is not made from pure gold. The gold cube is not pure gold as it is lighter than pure gold when it is at 8cm³. At 8cm³, the pure gold should weigh in at 154.4g. This gold cube weighs 120g which is lighter than the pure gold cube. Therefore, it is not pure gold.

4. 1a) 7/2
= \$3.50/litre

1b) 360/5
= 72 vases/day

1c) 376/8
= 47 words/min

1d) 240/3
= 80/m²

1e) 10/2.5
= 4kg/m

1f) 720/12
= 60g/egg

2a) 184/8
= \$23/hour

2b) 184 X 5
= \$920/week

3a) 225/25
= 9km/litre

3b) 30/25
= \$1.20/litre

4a) 525/6
= 87.5/cube

4b) 5x5x5=125 cm³
87.5/125
= 0.7g/cm³

5a) 120/8
= \$15/ticket

5b) 15 X 10
= \$150/10 tickets

6a) 270/12
= \$22.50/m²

6b) 22.50 X 20
= \$450/20m²

7a) 9 X 3
= 27litres/min

7b) 60 X 45 X 30 = 81,000 cm³ = 81 litres
81/27
= 3 minutes to fill the tank completely with water

8a) 13 X 2
= \$26/kg

8b) 500/20
= 25g/m²

8c) 15 X 8 = 120m²
500 X 6 = 3000g
= 3kg
\$13 X 6
= \$78

9a) 504,000/5 X 2
= \$201,600

9b) 504,000/120
= \$4200/m²

10a) 3 X 3 X 3 = 27cm³
52.11/27
= 19.3g/cm³

10b) 2 X 2 X 2 = 8cm³
120/8
= 15g/cm³

It is not made out of pure gold because it has a lower mass to cm³ rate than the 1st cube

5. 1. (a)\$3.50/litre
(b)72 vases/day
(c)47 words/min
(d)\$80 /m^2
(e)4kg /m
(f)60g /egg

2. (a)\$23 /hour
(b)\$92 0/week

3. (a)9 KM /litre
(b)\$1.20 /litre

4. (a)87.5g/cube
(b)0.7g/cm^3 of cube

5. (a)\$15 /ticket
(b)\$50

6. (a)\$22.50/m^2
(b)\$450

7. (a)27 liters/minute
(b)3 minutes

8. (a)\$26/Kg
(b)25g
(c)mass=3Kg
cost=\$78

9. (a)\$201000
(b)\$4200/m^2

10.(a)19.3g/cm^3

Explanation:
(b)its not made of pure gold because the gold cube's mass per cm^3 is 15 while the mass of pure gold per cm^3 is 19.3g.

6. Basic Practice
============
1 (a) \$7 / 2l = \$3.50/l

(b) 360 / 5 = 72vases/day

(c) 376words / 8minutes = 47words/min

(d) \$240 / 3m^2 = \$80/m^2

(e) 10kg / 2.5m = 4kg/m

(f) 720g / 12eggs = 60g/egg

2 (a) \$184 / 8hr = \$23/h

(b) \$184 X 5days(week) = \$920/week

3 (a) 225km / 25l = 9km/litre

(b) \$30 / 25l = \$1.2/l

4 (a) 525g / 6cubes = 87.5g/cube

(b) 5^3 = 125cm^3
87.5g / 125cm^3 = 0.7g/cm^3
-------------------------------
Further Practice
-------------------------------

5 (a) \$120 / 8tickets = \$15/ticket

(b) \$15 X 10 = \$150

6 (a) \$270 / 12m^2 = \$22.50/m^2

\$22.50 X 20m^2 = \$450

7 (a) 9l X 3 = 27l/min

(b) 60cm X 45cm X 30Cm = 81l
81l / 27l = 3mins

8 (a) \$13 X 2 = \$23/kg

(b) 500g / 20m^2 = 25g

9 (a) \$504000 / 5 X 2 = \$201600

(b) \$504000 / 120m^2 = \$4200/m^2

10 (a) 3x3x3=27
521.1g / 27cm^3 = 19.3g/cm^3

(b) Mass/cm^3 of the GOLD cube is 15g/cm^3
Mass/cm^3 of the PURE GOLD cube is 19.3g/cm^3
the both masses are different and therefore the other gold cube is not made of pure gold.

7. 1.
(a)\$3.5/litre
(b)72vases/day
(c)47words/min
(d)\$80/m^2
(e)4kg/m
(f)60g/egg

2.
(a)\$23/hour
(b)\$920/week

3.
(a)9km/litre
(b)\$1.20/litre

4.
(a)87.5g/cube
(b)4.2g/cm^2

5.
(a)\$15/ticket
(b)\$150/ticket

6.
(a)\$22.5/m^2
(b)\$450

7.
(a)27litre/min
(b)60x45x30 = 81000
81000÷1000 = 81
81÷27 = 3
3mins

8.
(a)\$261kg
(b)25g
(c)Mass:3Kg
Cost:\$78

9.
(a)\$201600
(b)\$4200/m^2

10.
(a)19.3g/cm^3
(b)pure gold cube = 174g/cm
"gold cube" = 60g/cm
No. The rate of the mass per cm of the "gold cube" is lesser than the pure gold cube, thus it is to light to be a gold cube.

8. 1a) \$7÷2=\$3.50 / l
1b) 360÷5=72 vases/day
1c) 376÷8=47 words/min
1d) \$240÷3m²=\$80/m²
1e) 10÷2.5=4 kg/m
1f) 720÷12=60 g/egg

2a) \$184÷8h=\$23/h
2b) \$184 x 5 days=\$920/week

3a) 225km÷25l =9km / l
3b) \$30÷25l =\$1.2 / l

4a) 525÷6=87.5g/cube
4b) 5m x 5cm x 5cm=125cm³

5a) \$120÷8=\$15/concert ticket
5b) \$15 x 10=\$150

6a) \$270÷12m²=\$22.50/m²
6b) \$22.50 x 20m²=\$450

7a) 9l /20s x 3=27l/min
7b) 60cm x 45cm x 30cm=40500ml 27l/min =27000ml/min 40500ml÷27000ml/min=1.5min

8a) \$13/500g x 2=\$26/kg
8b) 500g÷20=25g/m²
8c) 15m x 8m=120m² 120m² x 25g/m²=3000=3kg \$26/kg x 3kg=\$78

9a) \$504000÷5x2=\$201600
9b) \$504000÷120m²=\$4200/m²

10a) 3³cm=27cm³ 521.1÷27cm³=19.3g/m³
10b) No. Pure gold is 19.3g/m³, while the smaller cube of gold is 15g/m³, soit is not pure gold. 2³cm=8cm³ 120g÷8cm³=15g/m³

9. This comment has been removed by the author.

10. (1) ⎮ ANS
(1a)\$7 /2Litre
\$3.5/L
(1b)360 vases/5day
72vases/day
(1c)376 words/8minutes
47words/min
(1d)\$240/3m^2
\$80/m^2
(1e)10Kg/2.5m
4Kg/m
(1f)720g/12eggs
60g/egg

==================================================
(2)
(2a)\$184÷8=\$23
\$23/hr
(2b)\$184×5=\$920
\$920/week
==================================================
(3)
(3a)225Km÷25Litres
9Km/Litre
(3b)\$30÷25litres
\$1.20/litre
==================================================
(4)
(4a)525g÷6cubes
87.5g /cube
(4b)5cm×5cm×5cm
125 cm∗3
==================================================
(5)
(5a)\$120÷8tickets
\$15/ticket
(5b)\$15×10tickets
\$150
=================================================

11. 1a) \$3.50/l
1b) 72vases/day
1c) 47words/min
1d) \$80/m^2
1e) 4kg/m^2
1f) 60g/egg

2a) \$23
2b) \$920

3a) 9km/l
3b) \$1.20/l

4a) 87.5g
4b) 4.2g/cm^3

5a) \$15
5b) \$150

6a) \$22.5/m^2
6b) \$450

7a) 27l/min
7b) 3min

8a) \$26/kg
8b) 25g
8c) 3kg

9a) \$201600
9b) \$4200

10a) 19.3g/cm^3
10b) No. It is because the mass per cm^3 is only 15g/cm^3, not 19.3g/cm^3

12. (6)
(6a)\$270/12m*2
\$22.50
(6b)\$22.50x12
\$450
==================================================
(7)
(7a)9Litres x3
27litres
(7b)60cm x45cm x30cm=81000cm*3
81000cm*3/1000=81litres
81litres/9=9
9x20sec=180sec
ANS:180sec
==================================================
(8)
(8a)\$13x2
\$26
(8b)500g/20
25g
(8c)15mx8m=120m*2
120m*2/20=6
6x13=78
6x500=3000
ANS:
mass:3000g
cost:\$78
==================================================
(9)
(9a)504000x2/5=201600
\$201600
(9b)504000/120=4200
\$4200/m*2
==================================================(10)
(10a)3x3x3=27
521/27=19.39
ANS:19.39g/cm*3
(10b)2x2x2=8
120/8=15
15cm*3
the cube with the side of 2 cm is not pure gold as the cm*3 for pure gold is 19.39cm*3, but it is 15cm*3

13. 1a)\$3.50/l
b)72vases/day
c)47words/min
d)\$80/m*2
e)4kg/m
f)60g/egg

2a)\$23
b)\$920

3a)9km/l
b)\$1.20/l

4a)87.5g/cm*3
b)0.7g/cm*3

5a)\$15/ticket
b)\$150

6a)\$22.50/m*2
b)\$450

7a)27l/min
b)3min

8a)\$26/kg
b)25g/m*2
c)i)300g
ii)\$78

9a)\$201600
b)\$4200/m*2

10a)19.3g/cm*3
b)No. The mass of the pure gold cube is 19.3g/cm*3 while the mass of the gold cube is 15g/cm*3 which makes the gold cube lighter and is not pure gold as mass to volume ratio of pure gold to the gold cube is different.

14. Basic practice
--------------
1.
a) \$3.5/L
b) 72 vases/day
c) 47 words/min
d) \$80/m²
e) 4 kg/m
f) 60 g/egg

2.
a) \$23
b) \$920

3.
a) 9 km/L
b) \$1.2/L

4.
a) 87.5 g/cube
b) 0.7 g/cm³

5.
a) \$!5/ticket
b) \$150

6.
a) \$22.50/m²
b) \$450

7.
a) 27 L/min
b) 3 min

8.
a) \$13 x 2 = \$26
b) 25g
c) (15 x 8)m² = 120m²
mass = 25 x 120g = 3kg
cost = 26 x 3 = \$78

9.
a) 2/(2+3) x \$504000 = \$201600
b) \$504000 ÷ 120 = \$4200

10.
a) 521.1 ÷ 3³ = 19.3 g/cm³
b) 120 ÷ 2³ = 15 g/cm³

15. 1a)\$3.50 per litre
1b)72 vases per day
1c)47 words per min
1d)\$80/m²
1e)4kg/m
1f)60g/egg

2a)\$23/hr
2b)\$920/week

3a)9km/litre
3b)\$1.20/litre

4a)87.5g
4b)125cm³

5a)\$15
5b)\$150

6a)\$22.50/m²
6b)\$450

7a)27 litres/minute
7b)3 minutes

8a)\$26/kg
8b)25g
8c)3kg

9a)\$201600
9b)\$4200/m²

10a)19.3g/cm³
10b)No. It is because the mass of the cube per cm³ is only 15g/cm³, not 19.3g/cm³.Therefore, it is not pure gold.

16. 1) a) \$7 / 2 l = \$3.50/l l
b) 360 vases / 5 days = 72 vases/days
c) 376 words / 8 min = 47 words/min
d) \$ 240 / 3 m^2 = \$80 / m/62
e) 10 kg / 2.5 m^2 = 4kg / m^2
f) 720 g / 12 eggs = 60 g / g

2) a) \$/hours = \$184 / 8h = \$23/ h
b) \$/weeks = \$184 x / 1 weeks = \$920 / 1 week

3) a) km / litres = 225km / 25 l =9km/ litres
b) \$ / litres = \$ 30 / 25 l ~ (sry no equivalent sign) \$1.20/ litres

4 a) g/ cube = 525 g/ 6cubes = 87.5 g/ cube
b) g/ cm^3 = 87.5g / 5 x 5 x5 cm ^ 3 =
=87.5g / 125 cm^3
=0.7 g / m^3

5) a) \$ / Ticket = \$ 120 / 8 ticket = \$15/ ticket
b) \$15/ ticket x 10 = \$150

6) a) \$/ m ^ 2 = \$270 / 12 m^2
= \$22.5
b) \$22.50 / m^2 x 20 m^2 = \$450

7 ) a) 9 l /20s = 27 l /60s = 27 l / min
b) Time = Vol / Rate =
= (60 x 45 x 30 )cm ÷ 27 l /min
= 81000 cm ^ 3 ÷ 27 l / min
= 81 l ÷ 27 l / min

8) a) \$ / kg = \$13 / 500 g =\$13 / 0.5 kg
=\$ 26 / kg
b) g / m^2 = 500 g / 20m^2 =25g / m^2
c) Rate x m^2 = 25g /m ^2 x (15m x 8m)
= 3000g
Rate x kg = \$26 / kg x 3kg
= \$78

a) \$50400 x / (2 + 3) = \$201600
b) Rate : \$ /m^2 =\$504000 / 12 m^2
=\$4200 / m^2

10) a) Rate : g /cm ^3 = 521.1g /3 x3 x3 cm^3
= 521.1g / 27 cm^3
= 19.3 g/ cm ^3

b) Density: g /cm^3 = 120g /( 2 x 2 x 2)
= 15g/ cm ^ 3
No it is not, its density is different from pure gold

Sherman

17. 1a:\$3.50
1b:72 vases/day
1c:47words/min
1d:\$80/m^2
1e:4 kg/m
1f: 60 g/egg
2a:\$23/hour
2b:\$920/week
3a: 9km/litre
3b:\$3.30/litre
4a:87.5g/cube
4b:0.7 g
5a: \$15/ticket
5b:\$150
6a:\$22.50/m^2
6b:\$450
7a: 27 litre/min
7b: 3 min
8a:\$26
8b:25g
8c:\$1208
9a:\$201600
9b:\$4200/ m^2
10a:19.3g/cm^3
10b: no the density is 120g/cm^3 but a pure gold cube is 19.3g/cm^3

18. Charles O&#39;Rourke6/26/2011 08:22:00 PM

1. a)\$3.50/litre

b)72 vases/day

c)47 words/min

d)\$80/m2

e)4kg/m

f)6g/egg
-------------
2.a)\$23/hour

b)\$920/week

3.a)9 KM /litre

(b)\$1.20 /litre

4. (a)87.5g/cube

(b)0.7g/cm^3 of cube

5. (a)\$15 /ticket

(b)\$150

6. (a)\$22.50/m2

(b)\$450/

7. (a)27 l/min

(b)3 min

8. (a)\$26/Kg

(b)25g

(c)mass=3Kg
cost=\$78

9. (a)\$20100

(b)\$4200/m2

10.(a)19.3g/cm3

Explanation:
(b)The gold cube's mass for ever cm3 is 15 not 19.3g for every cm3 which is the pure gold;s mass

19. 1a. 3.50
1b. 72
1c. 47
1d. 80
1e. 4
1f. 60
2a. \$23/hour
2b. \$920/week
3a. 9km/litre
3b. \$1.20/litre
4a. 87.5g
4b. 125cm³
5a. \$15
5b. \$150
6a. \$22.50/m²
6b. \$450
7a. 27 litres/minute
7b. 3 minutes
8a. \$26/kg
8b. 25g
9a. \$201600
9b. \$4200/m²
10a.19.3g
10b. No, it is not. Pure gold's mass is 19.3g/cm3 but this gold in the gold cube has a mass of 15g/cm3 which is not the same as pure gold so it is not pure gold.

20. 1a.\$3.50/litre
1b.72 vases/day
1c.47words/min
1d.\$80/m^2
1e.4 kg/m
1f. 60 g/egg
2a.\$23/hour
2b.\$920/week
3a.9km/litre
3b.\$3.30/litre
4a.87.5g/cube
4b.0.7 g/m^3
5a.\$15/ticket
5b.\$150
6a.\$22.50/m^2
6b.\$450
7a. 27 litres/min
7b. 3 min
8a.\$26
8b.25g
8c.\$1208
9a.\$201600
9b.\$4200/ m^2
10a.19.3g/cm^3
10b. No, because the density of the gold cube is 15g/cm^3, while pure gold's is 19.3g/cm^3.